But they grew into the game and went close to drawing level when Teemu Pukki’s touch diverted Alex Tettey’s cross and goalkeeper Sam Johnstone had to react quickly to keep the ball out.
Albion began the second half as if keen to stretch their lead early, mindful perhaps of Norwich’s propensity for scoring late goals, but a second goal eluded them, despite the best efforts of Robson-Kanu and Gareth Barry, before Gayle blazed wide in a good position.
Albion needed a second goal but it did not come. Instead, the two Norwich substitutes combined to make the home crowd’s frustration feel so much worse, McLean’s low cross seeming to cause a moment’s hesitation in among the home defenders, enabling Rhodes to pounce.
Farke readily took credit for the match-winning change. “I’m really pleased for Jordan Rhodes. It’s great that he and Kenny McLean were able to come on and fulfil my ideas,” he said.
West Bromwich Albion (4-3-3): Johnstone; Holgate, Dawson, Hegazi, Gibbs; Harper, Barry, Brunt; Robson-Kanu (Leko 90+1), Rodriguez, Gayle (Sako 85).
Subs not used: Bond (g), Bartley, Hoolahan, Adarabioyo, Field.
Bookings: Barry, Rodriguez, Holgate.
Norwich City (4-2-3-1): Krul; Aarons, Zimmermann, Godfrey, Lewis (McLean 81); Tettey, Vrancic; Buendia (Srbeny 66), Cantwell (Rhodes 80), Hernandez; Pukki.
Subs not used: McGovern, Klose, Trybull, Thompson.
Bookings: Tettey, Buendia, Vrancic, Krul.